Kaehler extensions of Riemannian manifolds II
by
Alexei A. Krioukov
University of Wisconsin, Manitowoc

Any real analytic Riemannian manifold X of dimension n can be real analytically and isometrically embedded into a Kähler manifold [X\tilde] of the complex dimension n. Such a manifold [X\tilde] is then called a Kähler extension of X. In the paper the relationship between Riemannian manifolds and their Kähler extensions is explored. It is shown that the set of totally real, totally geodesic submanifolds having a given n-dimensional Kähler manifold as their Kähler extension is parametrized locally by the quotient U(n)/O(n) of the unitary and orthogonal groups. The question of existence of Ricci flat Kähler extensions is raised. In particular it is shown that every real analytic n-dimensional Riemannian manifold can be real analytically and isometrically embedded into a Ricci flat Riemannian manifold of dimension 4n.

Date received: March 25, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacr-25.